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fourier transform ans amplitude
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Hi everyone, good work, why is the converted signal divided by sqrt(n)^2 when finding P values after the Fourier transformation of the gaussian pulse on the matlab website?
Fs = 44100; % Sampling frequency
T = 1/Fs; % Sampling period
t = -0.5:T:0.5; % Time vector
L = length(t); % Signal length
X = 1/(0.4*sqrt(2*pi))*(exp(-t.^2/(2*(0.1*1e-3)^2)));
n = 2^nextpow2(L);
Y = fft(X,n);
f = Fs*(0:(n/2))/n;
P = abs(Y/sqrt(n)).^2; %???
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Hassaan
il 26 Feb 2024
Dividing by sqrt(n)^2 after performing the FFT on a Gaussian pulse or any signal in MATLAB is a normalization step to ensure that the signal's power or energy is consistently represented across the time and frequency domains, adhering to Parseval's theorem. This step is crucial for accurate signal analysis and interpretation in various scientific and engineering applications.
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